Research
Interests
·
Differential Equations and Dynamical
Systems
·
Mathematical Biology
·
Applied Mathematics
Current
research (supported by NSF-1021203):
·
A collaborative research with James
Cronin, John
Reeve and Mingqing Xiao: Development
time and predator-prey population dynamics.
Publications
(paper available upon email requests)
1. D.
Xu, J. D. Reeve, X. Wang and M.-Q. Xiao. Developmental
variability and stability in continuous-time host-parasitoid models.
Theoretical Population Biology, 78(1): 1-11, 2010.
2. D.
Xu and Z. Feng. A
metapopulation model with local competitions,
Discrete and Continuous Dynamical Systems (Series B), 12(2): 495-511,
2009.
3. Z.
Feng, Y. Yang, D. Xu, P. Zhang, M. McCauley,
M., J. W. Glasser. Timely identification of optimal
control strategies for emerging infectious diseases, J. Theoretical
Biology, 259: 165-171, 2009.
4. C.
Castillo-Chavez, Z. Feng and D. Xu. A schistosomiasis
model with mating structure and time delay, Mathematical
Biosciences, 211, 333-341, 2008.
5. Y.
Yang, D. Xu, Z. Feng. Analysis of a model with multiple infectious
stages and arbitrarily distributed stage durations, Math. Model.
Nat. Phenom. 3(7), 180-193, 2008.
6. Z.
Feng, D. Xu, H. Zhao. Epidemiological models with
non-exponentially distributed disease stages and applications to
disease control, Bulletin of Mathematical Biology, 69 (5),
1511-1536, 2007.
7. P.
Zhang, G. Sandland, Z. Feng, D. Xu, D. J. Minchella. Evolutionary implications for interactions
between multiple strains of host and parasite, J. Theoretical
Biology, 248, 225-240, 2007.
8. D.
Xu, Z. Feng, L. Allen and R. K. Swihart. A spatially
structured metapopulation model with patch
dynamics, J. Theo. Bio., 239, 469-481, 2006.
9. D.
Xu, J. Curtis, Z. Feng and D. J. Minchella. On the role
of schistosome mating structure in the
maintenance of resistant strains, Bulletin for Math. Bio., 67:
1207-1226, 2005.
10. D. Xu, X.-Q. Zhao. Dynamics
in a periodic competitive model with stage structure, J. Math.
Anal. Appl., 311: 417-438, 2005.
11. D. Xu, X.-Q. Zhao. Asymptotic
speed of spread and traveling waves for a nonlocal epidemic model,
Discrete Contin. Dynam.
Systems, 5: 1043-1058, 2005.
12. D. Xu. Global dynamics and Hopf bifurcation of a structured population model,
Nonlinear Analysis: Real World Applications, 6: 461-476, 2005.
13. D. Xu, X.-Q. Zhao. Bistable waves in an epidemic model, J. of
Dynamics and Differential equations, 16: 679-707, 2004.
14. D. Xu, X.-Q. Zhao. A
nonlocal reaction-diffusion population model with stage structure, Canad. Appl. Math. Quart., 11: 303-319, 2003.
15. Z. Jing, D. Xu, Y. Chang, L. Chen. Bifurcations, chaos, and system collapse in
a three-node power system, International J. of Electrical Power
Energy Systems, 25, 443-461, 2003.
16. Z.
Jing, K. Y. Chan, D. Xu, H. Cao. Bifurcations of periodic solutions and
chaos in Josephson system, Discrete Contin.
Dynam. Systems, 7(3): 573-592, 2001.
17. D. Xu, D. Meng. The model
and simulation of inhibition in the extrinsic path of blood
coagulation: the dynamic effects of protein C, Acta
Biophysica Sinica, 14:
657-665, 1998. (Chinese)
Finished or
on-going projects
·
M.-Q. Xiao, J. D. Reeve and D. Xu. Mean occupancy time for
biased edge movement between two different habitat types.
Submitted, 2010. (the paper available upon email requests)
·
Y. Chang, D. Xu
and Z. Jing. Complex dynamics in swing
equations of a power system model. Submitted 2010. (the paper
available upon email requests)
·
The role of tuberculosis in high HIV
prevalence populations. In preparation (with Z. Feng and M. Lannelli).
·
The role of drug treatments in the
evolutionary dynamics of complex host-parasite interactions. In
preparation (with Z. Feng, G. Sandland, D. J.
Minchella, Y. Yang).
Vita
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